If we take \(w_e=1\) , then \(A(H)\)  becomes the adjacency matrix of the unweighted hypergraph \(H(V,E)\)  defined in [1]}.
The valency of a vertex \(i\)  of \(H\) , denoted by \(d(i)\)  is defined as \(d(i)=\underset{e\in E;i\in e}{\sum }w_e\) .
The Laplacian matrix \(L(H)\)  of \(H(V,E,W)\)  is defined by \(L(H)=D(H)-A(H)\) , where \(D(H)\)  is the diagonal matrix whose entries are the valencies \(d(i)\)  of the vertices \(i\)  of \(H\) . If the hypergraph \(H(V,E,W)\)  has no isolated vertices, then
its normalized Laplacian matrix \(\mathcal {L}(H)\)  is defined as \(\mathcal {L}(H)=D(H)^{-1/2}L(H)D(H)^{-1/2}\) .
